Showing papers by "Moscow State University published in 1972"

Stability regions of dissipative trapped-ion instability

Abstract: Conditions for the stability of the dissipative trapped ion mode in axisymmetric toroidal confinement systems are investigated, and the ranges of temperature and magnetic field for which the plasma is expected to be unstable are calculated numerically for several proposed Tokamaks. The collisional damping is studied as a boundary layer problem in the velocity space of the trapped ions. The Fokker-Planck equation is solved by means of a variational form with the ordering νiR/r ω 2π/τi, where R/r is the aspect ratio, νiR/r is the effective collision frequency, and τi is the bounce time. The relative damping rate is found to be proportional to (νiR/rω) 1/2 [In (rω/νiR)1/2]−3/2 rather than νiR/rω. This damping term is compared with the electron driving term, which is proportional to rω/Rνe, and with the Landau damping caused by resonant untrapped ions. The presence of a temperature gradient is found to be destabilizing. The Landau term provides relatively strong damping when dT/dr=0 but changes sign when d ln T/d In n > 2/3. In the latter case it is concluded that ion collisions are insufficient to stabilize the mode under typical operating conditions of the proposed machines. Finally, if d ln T/d In n > 1.75 the ion collisional damping itself changes to growth, and the mode cannot be stabilized.

Medium-energy ion scattering by solid surfaces part II

Abstract: This paper is an attempt to systematize the experimental results obtained in studying medium- energy ion scattering by solid surfaces. We confine ourselves to the analysis of only one definite interval of primary ion energies-from several keV to several hundreds of keV. This is due to several reasons. First, only this energy interval has been investigated in most detail. Second, only in this interval are the experimental data obtained by various authors in a good agreement. Therefore one can draw well-founded conclusions concerning the mechanism of medium-energy ion scattering by solids. Finally, the scientific interest of the authors is of certain importance when choosing the given energy interval.

Finite automata and Burnside's problem for periodic groups

Abstract: New examples of infinite periodic finitely-generated groups are constructed. The elements of the groups are mappings of a set of words in an alphabet X into itself induced by finite Mealy automata. Estimates are given of the number of states and diagrams of the automata realizing the generating elements of the groups. There are three items in the literature cited.

Multiple scattering of channeled ions in crystals

Abstract: The Focker-Planck equation for scattering of channeled ions by electrons and thermal vibrations of crystalline lattice atoms has been obtained and solved. For calculations use is made of two models of the electron density distribution in a channel: the Thomas-Fermi model and the free-electron model. Axial and planar channeling is considered. It is shown that scattering by electrons plays an important part in ion dechanneling. In particular, in axial channeling scattering by electrons has a dominant effect on dechanneling of fast light ions. A comparison is made between theory and experiment on dechanneling of fast ions in tungsten and silicon.

On the Theory of Electroabsorption in Disordered Semiconductors

Abstract: The interband absorption coefficient is calculated for a disordered semiconductor subjected to an external electric field in the low-temperature case. Two kinds of random fields are considered, the “smooth” random field possessing a correlation function which is continuous and differentiable as many times as needed and that of the Coulomb field produced, for example, by the randomly distributed charged centres (compensated samples are considered). If the external field is low enough, the change in the exponential tail (ħω < ϵg) may be expressed in the form of a shiftedband edge Δϵg. When the external field becomes strong enough, the absorption coefficient takes on the well-known form deduced by Franz and Keldysh. In case of a “smooth” field the tail range in the electroabsorption coefficient is considered while in the Coulombic case graphs of the electroabsorption coefficient are plotted in the range of interest. The Redfield representation of an absorption coefficient of a disordered semiconductor is discussed. Der Interband-Absorptionskoeffizient eines ungeordneten Halbleiters in einem auseren elektrischen Feld wird im Falle tiefer Temperaturen berechnet. Zwei Arten von zufalligen Feldern werden betrachtet, der Fall eines glatten zufalligen Feldes mit einer kontinuierlichen und beliebig oft differenzierbaren Korrelationsfunktion und der eines Coulombfeldes, das zum Beispiel von zufallig verteilten geladenen Zentren verursacht wird (kompensierte Proben werden betrachtet). Falls das ausere Feld genugend schwach ist, kann die Ande-rung im exponentiellen Auslaufer (ħω < ϵg) in Form einer verschobenen Bandkante Δϵg dargestellt werden. Wenn das adere Feld genugend stark wird, nimmt der Absorptions-koeffizient die allgemein bekannte Form an, die von Franz und Keldysh ausgerechnet wurde. Im Falle eines glatten Feldes wird der Auslaufer im Elektroabsorptionskoeffizienten betrachtet, wahrend im Falle eines Coulombfeldes der Elektroabsorptionskoeffizient im interessierenden Bereich graphisch dargestellt wird. Die Redfield-Darstellung fur einen Absorptionskoeffizienten im ungeordneten Halbleiter wird diskutiert.

13C NMR spectra of metal σ-cyclopentadienyls

Abstract: Proton decoupled 13C NMR spectra have been measured for the cyclopentadienyl compounds C5H5Si(CH3)nCl3−n(n = 1, 2, 3), C5H5Ge(CH3)3, CH3C5H4Ge(CH3)3, C5H5Sn(CH3)3, σ-C5H5Fe(CO)2-π-C5H5 and C5H5HgCH3. A fast metallotropic rearrangement occurring in the compounds causes the spectra to be temperature dependent for the Si, Ge, Sn and Fe derivatives. For the derivatives of silicon or germanium, the olefinic signals are unsymmetrically broadened by the 1,2-shift at lower migration rates. Line widths of the ring carbon signals have been measured to give an estimate for the activation parameters of the rearrangement in C5H5Ge(CH3)3 (Ea = 10·7 ± 0·9 kcal/mole, ΔG‡ = 13·4 ± 0·9 kcal/mole) and C5H5Sn(CH3)3 (Ea = 6·8 ± 0·7 kcal/mole, ΔG‡ = 7·1 ± 0·7 kcal/mole). At room temperature, the spectrum of C5H5HgCH3 displays just one narrow signal responsible for the cyclopentadienyl ligand. The spectrum of CH3C5H4Ge(CH3)3 at –30° demonstrates that two isomers containing methyl in the vinylic position are present, the ratio being ca. 2:1. The 13C spectra of the vinylic isomers have been analysed in the case of C5H5Si(CH3)nCl3−n.

Optimal interpolation of analytic functions

Abstract: We construct an optimal interpolation formula for a particular class of analytic functions, optimization being over a set of interpolation methods which are not necessarily linear. Optimal nodes and the norm of the error are found for the optimal interpolation formula.

Energy transfer in bacterial photosynthesis. I. Light intensity dependences of fluorescence lifetimes.

Abstract: Four possible explanations are offered to account for low fluorescence increase observed for purple bacteria under transition from active to inhibited photosynthesis. The increase observed is inconsistent with high (≅1.0) yield of primary photosynthetic process of P890 photooxidation. The dependences of fluorescence yield and lifetime on the portion of active reaction centres have been analysed for each case. Experimental investigation carried out favours the existence of background fluorescence together with fluorescence, whose quantum yield correlates with the reaction centre functional state. The important conclusion is made that lifetime of photosynthetic fluorescence is much lower than 1 nsec and energy is transferred to the reaction centres by a mechanism other than inductive-resonance.

13C NMR spectra of cyclopropane derivatives. Stereoisomeric substituted 2‐phenylcyclopropanes

Abstract: Proton-decoupled carbon-13 magnetic resonance spectra of a series of cyclopropane derivatives have been studied. For stereoisomeric substituted 2-phenylcyclopropanes a difference between the isomers has been found in the shieldings of the three-membered cyclic carbons as well as in the shieldings of the carbons of the substituents. The chemical shifts have been interpreted on the basis of an additive approach worked out in a study of the spectra of monosubstituted cyclopropanes and substituted 2,2-diphenylcyclopropanes. Some simple rules have been proposed, which are useful in distinguishing stereoisomeric 1,2-disubstiuted cyclopropanes.

The study of streaming potentials on fissured media models

Abstract: In massive rocks ground waters mainly flow in fracture zones whose permeability greatly changes depending on their filling. When studying ground-water flow in fissures, the results of observations of the electric fields of filtrational origin—which, in this case, considerably differ from those in porous media—can be used. Therefore the authors have made experiments on fissured media models. The measurements have been made in a special filtration tube with the fissured media simulated by a system of quartz glass plates. The spacings between plates were regarded as fissure widths. The observations have been made in fully open “fissures” and in those partially filled with sand or sandy-clay material. These experiments have resulted in establishing a dependence between the values of streaming potentials and pressure drops. The SP values have particularly been found to decrease with the opening of “fissures”. The most intensive electro-filtrational fields were observed at 40 per cent filling with medium grained sand. Additions of argillaceous material to the sand filler brought about sharp reductions in the intensity of electro-filtrational potentials.

Hereditary and semi-hereditary monoids

Abstract: Left hereditary and semi-hereditary monoids are analogous to left hereditary and semi-hereditary rings. Necessary and sufficient conditions are given for the heredity and semi-heredity of arbitrary and commutative monoids.